A phenomenological renormalisable quantum field theory, which is an extension of SM and takes into account violation of Lorentz invariance (LIV) and the CPT theorem (CPTV), is known as the Standard Model extension [1]} (SME). The free fermion Lagrangian \(L_f\)  becomes
\(L_{f} & = & i\bar{\psi } \left( \gamma _{\mu } +c_{\mu \nu }\gamma ^{\nu } +d_{\mu \nu }\gamma _{5} \gamma ^{\nu } +e_{\mu }+if_{\mu }\gamma _{5} +\frac{1}{2} g_{\mu \nu \rho }\sigma ^{\nu \rho } \right) \partial ^{\mu } \psi \nonumber \\& &-\bar{\psi } \left( m+a_{\nu }\gamma ^{\nu } +b_{\nu }\gamma _{5} \gamma ^{\nu } +\frac{1}{2} H_{\nu \rho }\sigma ^{\nu \rho } \right) \psi \) 
